(Reuters) - Warren Buffett's Berkshire Hathaway Inc , the largest investor in DaVita HealthCare Partners Inc , has entered an agreement allowing it to nearly double its stake in the largest U.S. operator of dialysis clinics to 25 percent.

According to a regulatory filing, the companies on Tuesday entered a "standstill" agreement, which is often used to prevent unsolicited takeovers, indicating the maximum percentage of shares that Berkshire can own.

DaVita shares rose $3.84, or 3.3 percent, to $121.40 in after-hours trading after the agreement was disclosed.

Berkshire owned about 15 million DaVita shares, or 14.2 percent, as of March 4, according to another regulatory filing.

These shares were worth about $1.76 billion, based on Tuesday's closing price of $117.56 for DaVita. That price gave DaVita a market value of about $12.4 billion.

Buffett's company ended March with $49.1 billion of cash, of which $12.1 billion is being used to help fund the pending purchase of ketchup maker H.J. Heinz Co

DaVita has long been a favorite investment of Ted Weschler, one of two portfolio managers Buffett hired to run portions of Berkshire's $95.9 billion portfolio of equities.

Buffett recently gave Weschler and the other portfolio manager, Todd Combs, an additional $1 billion each to invest.

Within the last five years, Berkshire has held stakes exceeding 20 percent in railroad operator Burlington Northern Santa Fe Corp, which it later bought, and credit rating company Moody's Corp , whose shares it has recently been selling.

Separately, Denver-based DaVita reported on Tuesday an adjusted first-quarter operating profit excluding a legal reserve of $196.9 million, or $1.84 per share. Analysts on average expected $1.79 per share, according to Thomson Reuters I/B/E/S.